Grade 2 Mathematics Curriculum Document 2016-2017

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Grade 2 Mathematics Curriculum Document

2016-2017

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Table of Contents Cover Page Pg. 1 Table of Contents Pg. 2 Trouble Shooting Guide Pg. 3 Best Practices in the Math Classroom Pg. 4 Problem Solving 4-Square Model Pg. 6 Problem Solving with Pictorial Modeling/ Strip Diagrams Pg. 7 Number Sense/ Number Talks Pg. 8 Year at a Glance Pg. 11 Mathematics Process Standards Pg. 12 Math Instructional Resources Pg. 13 Bundle 1: Basic Fact Strategies and Problem Solving Pg. 14 Bundle 2: Representing and Comparing Whole Numbers to 1,200 Pg. 19 Bundle 3: 2-Digit Addition and Subtraction (Strategies and Problem Solving) Pg. 28 Bundle 4: Money Pg. 35 Bundle 5: Understanding Contextual Multiplication and Division Pg. 39 Bundle 6: Data Analysis Pg. 44 Bundle 7: 3-Digit Addition and Subtraction (Strategies and Problem Solving) Pg. 50 Bundle 8: Exploring the Addition and Subtraction Algorithms and Problem Solving Pg. 57 Bundle 9: Geometry Pg. 64 Bundle 10: Fractions Pg. 70 Bundle 11: Measurement Pg. 75 Bundle 12: Personal Financial Literacy Pg. 82 Bundle 13: Extended Learning Pg. 88

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Trouble Shooting Guide

• The 2015-2016 Mathematics Curriculum Document for Grade 2 includes the following features:

• The NISD Curriculum Document is a TEKS-Based Curriculum.

• Year at a Glance Indicating Bundle Titles and Number of Days for Instruction

• Color Coding: Green- Readiness Standards, Yellow- Supporting Standards, Blue- Process Standards,

Purple- ELPS, Strike-Out- Portion of TEKS not Taught in Current Bundle

• NISD Math Instructional Focus Information

• The expectation is that teachers will share additional effective resources with their campus Curriculum &

Instructional Coach for inclusion in the document.

• The NISD Curriculum Document is a working document. Additional resources and information will be

added as they become available.

• **Theresourcesincludedhereprovideteachingexamplesand/ormeaningfullearningexperiencestoaddresstheDistrictCurriculum.InordertoaddresstheTEKStotheproperdepthandcomplexity,teachersareencouragedtouseresourcestothedegreethattheyarecongruentwiththeTEKSandresearch-basedbestpractices.Teachingusingonlythesuggestedresourcesdoesnotguaranteestudentmasteryofallstandards.Teachersmustuseprofessionaljudgmenttoselectamongtheseand/orotherresourcestoteachthedistrictcurriculum.

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NISD Math Focus

Best Practices in the Math Classroom • Teaching for Conceptual Understanding: Math instruction should focus on developing a true understanding of the math concepts being

presented in the classroom. Teachers should avoid teaching “quick tricks” for finding the right answers and instead focus on developing student understanding of the “why” behind the math. Math is not a list of arbitrary steps that need to be memorized and performed, but is, rather, a logical system full of deep connections. When students see math as a set of disconnected steps to follow they tend to hold many misconceptions, make common mistakes, and do not retain what they have learned. However, when students understand the connections they have fewer misconceptions, make less errors, and tend to retain what they have learned.

• Developing Student Understanding through the Concrete-Pictorial-Abstract Approach: When learning a new math concept, students should be taken through a 3-step process of concept development. This process is known as the Concrete-Pictorial-Abstract approach. During the concrete phase, students should participate in hands-on activities using manipulatives to develop an understanding of the concept. During the pictorial phase, students should use pictorial representations to demonstrate the math concepts. This phase often overlaps with the concrete phase as students draw a representation of what they are doing with the manipulatives. During the abstract phase, students use symbols and/or numbers to represent the math concepts. This phase often overlaps with the pictorial phase as students explain their thinking in pictures, numbers, and words. If math concepts are only taught in the abstract level, students attain a very limited understanding of the concepts. However, when students go through the 3-step process of concept development they achieve a much deeper level of understanding.

• Developing Problem Solving Skills through Quality Problem Solving Opportunities: Students should be given opportunities to develop their problem solving skills on a daily basis. One effective approach to problem solving is the think-pair-share approach. Students should first think about and work on the problem independently. Next, students should be given the opportunity to discuss the problem with a partner or small group of other students. Finally, students should be able to share their thinking with the whole group. The teacher can choose students with different approaches to the problem to put their work under a document camera and allow them to talk through their thinking with the class. The focus of daily problem solving should always be Quality over Quantity. It is more important to spend time digging deep into one problem than to only touch the surface of multiple problems.

• Developing Problem Solving Skills through Pictorial Modeling: One of the most important components of students’ problem solving development is the ability to visualize the problem. Students should always draw a pictorial representation of the problem they are trying to solve. A pictorial model helps students to better visualize the problem in order to choose the correct actions needed to solve it. Pictorial modeling in math can be done with pictures as simple as sticks, circles, and boxes. There is no need for detailed artistic representations. One of the most effective forms of pictorial modeling is the strip diagram (or part-part-whole model in lower grades). This type of model allows students to see the relationships between the numbers in the problem in order to choose the proper operations.

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• Developing Students’ Number Sense: The development of number sense is a critical part of a student’s learning in the mathematics classroom. The ability to reason about numbers and their relationships allows students the opportunity to think instead of just following a rote set of procedures. The standard algorithms for computation may provide students with a quick answer, but they do not allow for development of student thinking and reasoning. The standard algorithms should not be abandoned completely, but should be used as one of many ways of approaching a computation problem. It is, however, very important that students have the opportunity to develop their number sense through alternative computation strategies before learning the standard algorithm in order to prevent students from having a limited view of number relationships.

• Creating an Environment of Student Engagement: The most effective math classrooms are places in which students have chances to interact with their teacher, their classmates, and the math content. Students should be given plenty of opportunities to explore and investigate new math concepts through higher-order, rigorous, and hands-on activities. Cooperative learning opportunities are critical in order for students to talk through what they are learning. The goal should be for the student to work harder than the teacher and for the student to do more of the talking.

• Higher Level Questioning: The key to developing student thinking is in the types of questions teachers ask their students. Teachers should strive to ask questions from the top three levels of Bloom’s Taxonomy to probe student thinking.

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NISD Math Focus

Developing Problem Solving through a 4-Square Model Approach • The 4-square problem solving model should be used to help guide students through the problem solving process. It is important that

students complete step 2 (pictorial modeling) before attempting to solve the problem abstractly (with computation). When students create a visual model for the problem they are better able to recognize the appropriate operation(s) for solving the problem.

Dragon Problem Solving What does the question ask me?

This is the picture in my mind.

This is how I solve the problem.

I know I am right because...

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NISD Math Focus

Developing Problem Solving through Pictorial Modeling/ Strip Diagrams • Visual models for addition and subtraction situations help students see relationships between quantities. In the model, students place

object, then later draw dots, then later write numbers.

Joining/ Combining There are 3 birds. 2 more fly in. How many birds in all?

?

There are 3 birds. More fly in. Then there are 5 in all. How many flew in?

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There are some birds. 2 more fly in. Then there are 5 in all. How many were there to begin with?

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Separating There are 7 birds. 3 birds fly away. How many are left?

7 3 ?

There are 7 birds. Some fly away. Then 4 birds are left. How many flew away?

7 ? 4

There are some birds. 3 birds fly away. Then 4 birds are left. How many were there to begin with?

? 3 4

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NISD Math Focus

Developing Number Sense through Number Talks What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.

A Rationale for Number Talks

http://www.mathsolutions.com/documents/9781935099116_ch1.pdf

Number Talks 6-Weeks Strategy Focus

Operation Strategies 1st 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each

Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

2nd 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

3rd 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

4th 6-Weeks Addition Doubles/Near Doubles, Making 10s, Making Landmark or Friendly Numbers, Breaking Each Number into Its Place Value (Decomposing Each Number), Compensation, Adding Up in Chunks (Decomposing One Number)

5th 6-Weeks Subtraction Adding Up, Removal/ Counting Back 6th 6-Weeks Subtraction Adding Up, Removal/ Counting Back

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Number Talks

Addition and Subtraction Strategy Examples

Operation Strategy Example Addition Doubles/ Near Doubles Use a known double to solve an unknown near-double

8 + 8 = 16 8 + 9 = 17 because 8 + 9 is the same as 8 + (8 + 1) or (8 + 8) + 1 8 + 7 = 15 because 8 + 7 is the same as 8 + (8 – 1) or (8 + 8) - 1

Addition Making Tens Decompose a number to make a ten 8 + 4 = 8 + (2 + 2) = (8 + 2) + 2 = 10 + 2 = 12

8 + 2 = 10 10 + 2 = 12

Addition Making Landmark or Friendly Numbers

Decompose a number to make a friendly number (usually a multiple of 10) 19 + 15 = 19 + (1 + 14) = (19 + 1) + 14= 20 + 14 = 34

19 + 1 = 20 20 + 14 = 34

Addition Breaking Each Number into Its Place Value (Decomposing Each Number)

24 + 21

20 + 20 = 40 4 + 1 = 5 40 + 5 = 45

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Addition Compensation 18 + 23

18 + 23 +2 - 2 20 + 21 = 41

36 + 9

36 + 9 - 1 +1 35 + 10 = 45

Addition Adding Up in Chunks (Decomposing One Number)

35 + 42 35 + 10 = 45 45 + 10 = 55 55 + 10 = 65 65 + 10 = 75 75 + 2 = 77

Subtraction Adding Up 40 – 28 = ____ or 28 + ____ = 40

28 + 2 = 30 30 + 10 = 40 28 + 12 = 40 so 40 – 28 = 12

Subtraction Removal/ Counting Back 45 – 28

45 – 10 = 35 45 – 10 = 25 25 – 5 = 20 20 – 3 = 17

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Year at a Glance First Semester Second Semester 1st 6-Weeks 4th 6-Weeks

• Bundle #1- Basic Fact Strategies and Problem Solving (14 days) • Bundle #2- Representing and Comparing Whole Numbers to

1,200 (15 days)

• Bundle #7- 3-Digit Addition and Subtraction (Strategies and Problem Solving) (14 days)

• Bundle #8- Exploring the Addition and Subtraction Algorithms

and Problem Solving (10 days)

• Bundle #9- Geometry (4 days) 2nd 6-Weeks 5th 6-Weeks

• Bundle #2 (cont.)- Representing and Comparing Whole Numbers to 1,200 (4 days)

• Bundle #3- 2-Digit Addition and Subtraction (Strategies and Problem Solving (15 days)

• Bundle #4- Money (10 days)

• Bundle #9 (cont.)- Geometry (10 days)

• Bundle #10- Fractions (15 days)

• Bundle #11- Measurement (8 days)

3rd 6-Weeks 6th 6-Weeks • Bundle #4 (cont.)- Money (5 days)

• Bundle #5- Understanding Contextual Multiplication and

Division (15 days)

• Bundle #6- Data Analysis (9 days)

• Bundle #11 (cont.)- Measurement (10 days)

• Bundle #12- Personal Financial Literacy (10 days)

• Bundle #13- Extended Learning (8 days)

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Mathematical Process Standards • Process standards MUST be integrated within EACH bundle to ensure the success of students.

2.1A 2.1B 2.1C 2.1D 2.1E 2.1F 2.1G apply mathematics to problems arising in everyday life, society, and the workplace

use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

create and use representations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

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Math Instructional Resources

Resource Print/Online Description EnVision Both Textbook Adoption https://www.pearsontexas.com/#/ Motivation Math Both Supplemental Curriculum https://www.mentoringminds.com/customer/account/login/ Engaging Mathematics Print Collection of Mini-Lessons for All TEKS from Region IV http://www.region4store.com/catalog.aspx?catid=1171582 Thinking Blocks Online Online Problem Solving Practice with Strip Diagrams http://www.mathplayground.com/thinkingblocks.html 2nd Grade Math Games Print Collection of Engaging and Low-Prep Math Games for Skill Practice http://maccss.ncdpi.wikispaces.net/file/view/2ndgrade_GAMES.pdf/522022874/2ndgrade_GAMES.pdf Epic! For Educators Online Search for Literature Connections for Math Content https://www.getepic.com/educators Number Talks (Sherry Parrish) Print Develop Number Sense Through a Daily Number Talk Routine Lessons for Learning (North Carolina) Print Collection of Engaging and Rigorous Math Lessons http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade2.pdf/464833262/CCSSMathTasks-Grade2.pdf Math Learning Center (Bridges) Print Collection of Engaging and Rigorous Math Lessons http://catalog.mathlearningcenter.org/catalog/supplemental-materials-elementary/lessons-activities-grade-2-free NCTM Illuminations Online Search for Engaging and Rigorous Math Lessons by Grade and Topic http://illuminations.nctm.org/ Math Coach’s Corner Online Math Blog from a Master Texas Math Teacher, Coach, and Consultant http://www.mathcoachscorner.com/ Promethean Planet Online Tools and Lessons for Interactive Whiteboard http://www.prometheanplanet.com/en-us/ Interactive Math Glossary Online TEA Interactive Math Glossary http://www.texasgateway.org/resource/interactive-math-glossary?field_resource_keywords_tid=math%20teks&sort_by=title&sort_order=ASC&items_per_page=5

TEKS Information for Teachers TEA Math Resources Online TEA Supporting Information for Math TEKS http://tea.texas.gov/Curriculum_and_Instructional_Programs/Subject_Areas/Mathematics/Resources_for_the_Revised_Mathematics_TEKS/ Lead4Ward Resources Online Math TEKS Instructional Resources and Supporting Information http://lead4ward.com/resources/ TEKS Resource System Online Math TEKS Instructional Resources and Supporting Information http://www.teksresourcesystem.net/module/profile/Account/LogOn

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Course: Grade 2 Math Bundle 1: Basic Fact Strategies and Problem Solving

Dates: August 22nd -September 9th (14 days)

TEKS

2.4A: recall basic facts to add and subtract within 20 with automaticity 2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1B: monitor oral and written language production and employ self-corrective techniques or other resources Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency Reading 4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary Add/addition Difference Number sentence Sum Unknown Basic facts Equation Subtract/subtraction Term

Cognitive Complexity Verbs: recall, represent Academic Vocabulary by Standard: 2.4A: add, basic facts, difference, subtract, sum 2.7C: addition, difference, number sentence, equation, subtraction, sum, term, unknown

Suggested Math Manipulatives

Cuisenaire Rods Dice Dominoes Hundreds Chart Part/Whole Mat Number Lines Counters Rekenreks Ten Frames Snap Cubes

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Bundle 1: Vertical Alignment

1.3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10

2.4A: recall basic facts to add and subtract within 20 with automaticity

3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

1.5D represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences 1.5E understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s) 1.5F determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation

2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations 4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

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Bundle 1: Teacher Notes

TEKS/Student Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information

2.4A: recall basic facts to add and subtract within 20 with automaticity

In conjunction with 1.3D, students will continue to apply the following strategies to recall basic facts: Addition: - Make Ten with the use of two tens frames as a model

(i.e. 9 + 8 = ___; can be rewritten as

9 + 1 + 7 = ___; 10 + 7 = 17) - Make Ten with the use of an open number line

(i.e. 9 + 8 = ___; 9 + 1 + 7 = ___; 10 + 7 = ___; 10 + 7 = 17) - Doubles: (i.e. 6 + 8 = 6 + 6 + 2 = ___; 12 + 2 = ___; 12 + 2 = 14) - Count On: (i.e. 3 + 8 = ___; 8, 9, 10, 11; 3 + 8 = 11) Subtraction: - Think Addition/ Count One: (i.e. 12 – 9 = ___; 9 + ___ = 12; 9 + 3 = 12). - Make Ten: (i.e. 12 – 9 = 12 – 2 – 7 = 10 – 7 = 3). - Compensation (i.e. 12 – 9 = 12 - 10 + 1 = 2 + 1 = 3).

Efficiency and accuracy with basic addition/subtraction facts will be a critical foundation for students to be able to solve multi-step addition and subtraction problems using place value strategies. 2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =) 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms

The level of skill with “automaticity” requires quick recall of basic facts within 20 with speed and accuracy at an unconscious level. Automaticity is part of procedural fluency and, as such, should not be overly emphasized as an isolated skill. Automaticity with basic addition and subtraction facts allows students to explore richer applications of addition and subtraction. When paired with 2.1A, students may be expected to apply these basic facts.

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- Count Back: (i.e. 12 – 3 = ___; 12, 11, 10, 9; 12 – 3 = 9) In adherence to this grade level standard, students will continue to practice using these strategies in order to recall their basic facts with automaticity.


In conjunction with 2.4, students continue to demonstrate their understanding of addition and subtraction with the appropriate number sentence. Instruction should vary the context of +/- type problems provided to students (see 2.4C for examples). In adherence to the standard, students should represent the same word problem with a variety of number sentences (i.e. 17 + 18 = ___; 18 + 17 = ___; ___ = 18 + 17; ___ = 17 + 18); (i.e. 42 – 16 = ___; ___ = 42 – 16; 16 + ___ = 42; 42 = ___ + 16).

Relating addition and subtraction number sentences/equations supports a student’s ability to represent and solve addition and subtraction problems. 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

When paired with 2.1C and 2.1D, the students are expected to represent problems with objects, manipulatives, diagrams, language, and number. Students may be expected to solve problems using number sense, mental math, and algorithms based on place value and properties of operations. For example, Jasmine has 87 books. She has some paperback books and 39 hardback books. How many paperback books does Jasmine have? Represent: 87 = { } + 39

Solve: 87 = 40 + 40 + 7 = 39 + (1 + 40 + 7) = 39 + 48

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Course: Grade 2 Math Bundle 2: Representing and Comparing Whole Numbers to 1,200

Dates: September 12th-October 7th (19 days)

TEKS 2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones 2.2B: use standard, word, and expanded forms to represent numbers up to 1,200 2.2C: generate a number that is greater than or less than a given whole number up to 1,200 2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =) 2.2E: locate the position of a given whole number on an open number line 2.2F: name the whole number that corresponds to a specific point on a number line 2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number 2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200 2.9C: represent whole numbers as distances from any given location on a number line

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of

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social and grade-appropriate academic topics Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary 10 less Equal to (=) Hyphen Ones Standard form 10 more Even Least to greatest Open number line Tens 100 less Expanded form Less than (<) Pairing Thousands 100 more Greater than (>) Location Period Whole numbers Digit Greatest to least Number line Place value Word form Distance Hundreds Odd

Cognitive Complexity Verbs: use, compose, decompose, represent, generate, compare, order, locate, name, determine Academic Vocabulary by Standard: 2.2A: digit, place value, thousands, hundreds, tens, ones 2.2B: digit, expanded form, hyphen, period, place value, thousands, hundreds, tens, ones, standard form, word form2.2C: digit, greater than, less than, equal to, place value, value of a number 2.2D: digit, equal to (=), greater than (>), greatest to least, less than (<), least to greatest, place value, thousands, hundreds, tens, ones 2.2E: open number line, place value, whole numbers 2.2F: number line, place value, whole numbers2.7A: even, odd, pairing 2.7B: place value, ten more, ten less, 100 more, 100 less2.9C: distance, location, number line, place value, whole numbers


Base 10 Blocks Place Value Disks Place Value Chart Hundreds Chart Counters Snap Cubes Number Lines

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K.2I compose and decompose numbers up to 10 with objects and pictures 1.2B use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones

2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate 4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

1.2C use objects, pictures, and expanded and standard forms to represent numbers up to 120

2.2B: use standard, word, and expanded forms to represent numbers up to 1,200

3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate 4.2B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

K.2F generate a number that is one more than or one less than another number up to at least 20 1.2D generate a number that is greater than or less than a given whole number up to 120

2.2C: generate a number that is greater than or less than a given whole number up to 1,200

K.2G compare sets of objects up to at least 20 in each set using comparative language K.2H use comparative language to describe two numbers up to 20 presented as written numerals 1.2E use place value to compare whole numbers up to 120 using comparative language 1.2F order whole numbers up to 120 using place value and open number lines 1.2G represent the comparison of two numbers to 100 using the symbols >,

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >,<,= 4.2C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >,<,= 4.2F compare and order decimals using concrete and visual models to the hundredths

1.2F order whole numbers up to 120 using place value and open number lines

2.2E: locate the position of a given whole number on an open number line

3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines. 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 4.2G represent fractions and decimals to the tenths or

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hundredths as distances from zero on a number line 4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

1.2F order whole numbers up to 120 using place value and open number lines

2.2F: name the whole number that corresponds to a specific point on a number line

3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines. 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line 4.2G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line 4.2H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

1.5B skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set

2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number

1.5C use relationships to determine the number that is 10 more and 10 less than a given number up to 120

2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

2.9C: represent whole numbers as distances from any given location on a number line

3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line

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2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones

Through the use of base 10 blocks, students will begin to visually understand the magnitude of numbers (i.e. the thousand cube is ten times more than the hundred flat; the hundred flat is ten times more than the ten rod; the hundred flat is ten times smaller than the thousand cube, the ten rod is ten times smaller than the hundred flat, etc.). Students need to understand that the digit in the number represents its place value which is different from the value of the number (i.e. the number 259 can be represented as 5 hundreds, 8 tens, 9 ones or 4 hundreds, 18 tens, and 9 ones, or 5 hundreds, 7 tens, and 19 ones, etc.). This understanding will lend itself to regrouping in subtraction (i.e. 589 – 192 = ___; 589 would have to be regrouped into 4 hundreds, 18 tens, and 9 ones).

The use of concrete objects (base 10 blocks) and pictorial models to represent numbers through 1,200 will support students’ conceptual understanding of the magnitude of numbers and the relationship between the place values. This knowledge will extend to relating those visual representations to expanded notation, supporting the comparing/ ordering of numbers, and developing addition/ subtraction place value algorithms. 2.2B: use standard, word, and expanded forms to represent numbers up to 1,200

Specificity for representations is included with the use of concrete and pictorial models to compose and decompose numbers. Specificity is included with “sum of so many thousands, hundreds, tens, and ones.” It may include decomposing 787 into 7 hundreds, 8 tens, and 7 ones. It may also include decomposing 787 into the sum of 500, 200, 50, 30, and 7 to prepare for work with compatible numbers when adding whole numbers with fluency. Students are expected to compose and decompose numbers up to 1,200. Students are expected to use pictorial models in addition to concrete models.

2.2B: use standard, word, and expanded forms to represent numbers up to 1,200

As students begin representing numbers through 1,200 using base ten blocks (see 2.2A), their understanding should also be associated with writing numbers in standard form (827), word form (eight hundred twenty-seven), and expanded form (i.e. 827 = 800 + 20 + 7). This type of representation will allow students to focus on the value of each digit and support the understanding of the place value system (i.e. eight flats represent the value 800; two ten rods represent the value of 20; seven unit cubes represent the value of 7; 800 + 20 + 7 = 827). AS grade 2 introduces the thousands period, it will be essential to explain the use of the comma to separate the periods (i.e. 1,243: the comma separates the hundreds period from the

* Students may incorrectly use the word “and” to represent numbers in words (i.e. 345 is represented as “three hundred forty-five,” not “three hundred and forty-five). The use of the word “and” is applied in the representations of whole number and decimal values (i.e. 3.45 is represented as “three and forty-five hundredths). * Students may not use the

Specificity is included for what is to be represented (read, written, and described): “standard, word, and expanded forms” to indicate place value. Students are expected to represent numbers up to 1,200.

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thousands period). In representing numbers in word form, be sure to emphasize the correct use of the hyphen (i.e. twenty-three).

hyphen appropriately when representing numbers in words (i.e. 345 is represented as “three hundred forty-five”). * Students confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value but it is valued at 40). * Students may confuse the term digit and number.

Standard Form

787

Word Form

Seven hundred eighty-seven

Expanded Form

700 + 80 + 7

2.2C: generate a number that is greater than or less than a given whole number up to 1,200

As students become more knowledgeable with their use of the place value system in using base-ten blocks (2.2A) and expanded notation (2.2B), instruction should include students generating a number “greater than” or “less than” a given whole number. Students should be able to explain that the position of each digit in a numeral determines the quantity of a given number (i.e. given the number 437, students understand that the digit four represents the number of hundred flats and its value 400; the digit three represents the number of ten rods and its value 30). This explanation is important to ask of children before they begin abstractly comparing two given numbers (2.2D) so students can demonstrate understanding of place value.

Generating a number greater than or less than a given whole number will allow students to focus on the value of various digits in a number before moving to the abstract use of comparison symbols (<, >, =). 2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

This SE extends K.2F where students are expected to generate a number that is one more or one less than another number up to 20 and 1.5C where students are expected to determine the number that is 10 more and 10 less than a given number up to 120.

2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

As students compare the value of numbers, they need to be able to relate their understanding of place value (i.e. the number 342 is greater than 226 because the digit 3 in 342 means there are 3 hundreds which is a value of 300. However, the digit 2 in 226 means there are only 2 hundreds and has a value of 200). Using expanded notation 300 + 40 + 2 is greater than 200 + 20 + 6. Students will compare two numbers using the correct academic vocabulary (i.e. 342 is greater than 226). It is important for students to recognize the inverse comparison statement as well (i.e. 226 is less than 342). The use of the comparative language is critical before moving

* Students who rely on a trick to determine the direction of an inequality sign may not be able to read comparison symbols correctly. * Students may view a comparison statement and its inverse as two different comparison statements (i.e. 456 > 412 is the same as 412 < 456).

Students are expected to compare and order numbers up to 1,200. Comparative language includes greater than, less than, and equal to.

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to the symbolic representation. It is important for students to recognize how their language can be communicated using symbols (<, >, =). It is critical that students do not learn how to read each of the symbols using a tricks to remember directionality of the symbols (i.e. the alligator’s mouth eats the bigger number). Encourage students to write and articulate two comparison statements during activities (i.e. 342 > 226 and 226 < 342). The standard also has students ordering three or more numbers from least to greatest or greatest to least. The use of open number lines (see 2.2E/F) will allow students to order more efficiently. The increase in the value of numbers from left to right on a number line can be associated to ordering from least to greatest; numbers decrease from right to left on a number line can be associated to ordering from greatest to least.

* Students confuse the place value a digit is in with its value (i.e. 345; the digit 4 is in the tens place value, but it is valued at 40). * Students may confuse the term digit and number.

2.2E: locate the position of a given whole number on an open number line

An open number line does not have landmark numbers earmarked, does not have to begin at zero, and should include the use of arrows on both ends of the number line to indicate that the numbers continue beyond what is marked.

Studentswillapplytheirunderstandingoftheplacevaluesysteminrelationtotherelativepositiononanopennumberline(i.e.thenumber352wouldfallbetween350and360onanumberlineas352isexpressedas300+50+2orthenumber352is3hundreds,5tens,and2ones).Asstudentsaregivenaspecificnumbertolocateonanopennumberline,youwillbegintoassessstudents’understandingofplacevalue(i.e.studentsplacethenumber352between350and360),therelativepositionofnumbers(i.e.thenumber350wouldbeindicatedfirstandthenumber360wouldbeindicatedsecondontheopennumberline),andthemagnitudeofnumbers(i.e.studentswouldphysicallyplacethenumber352closerto350than360).

Students can use number lines to compare/ order numbers and develop their understanding of place value, the relative position of numbers, and magnitude of numbers. The use of this tool is a critical support mechanism. 2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

This SE extends 1.2F where students are expected to order whole numbers up to 120 using place value. The use of an open number line as a representation allows for the consideration of the magnitude of numbers and the place-value relationships among numbers when locating a given whole number.

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2.2F: name the whole number that corresponds to a specific point on a number line

In contrast to 2.2E, specific numbers are already marked on this number line, did not have to begin at zero, and include the use of arrows on both ends of the number line to indicate how the numbers continue beyond what is marked.

Students will be provided a specific location identified on a given number line and asked to name the whole number representing its value. In conjunction with 2.2E, this activity will allow you to assess students’ understanding of place value, the relative position of number and the magnitude of numbers.

As a number line is used as a strategy to compare/order numbers and develops a student’s understanding of place value, the relative position of numbers, and the magnitude of numbers, the use of this tool will be a critical support mechanism. 2.2D: use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

This SE and 2.9C are introductory skills that build to the various number line skills in grade 3, including 3.2C, 3.3B, and 3.3F.

2.7A: determine whether a number up to 40 is even or odd using pairings of objects to represent the number

In order to adhere to the standard, students should be provided a set of objects to group in pairs to determine if a number is even or odd. As students begin pairing objects, instruction should relate this concept to the double facts (i.e. 18 is even as there are 9 groups of pairs (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18); 15 is odd as there are 7 groups of pairs with one left over (2 + 2 + 2 + 2 + 2 + 2 + 2 + 1 = 15).

As students solve problems using all operations, developing patterns with even and odd solutions can support students with their computational fluency and accuracy (i.e. odd + odd = even; even + odd = odd; odd – odd = even; odd – even = odd).

This SE provides a foundation for 3.4I.

2.7B: use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

In order to adhere to the standard, students must be able to determine 10 more/ 10 less or 100 more/ 100 less (i.e. using your 100s chart, what is 10 more than 23 or what is 10 less than 45?) As students move down a row to model ten more than a number, they should begin relating how the digit in the tens place is increasing by one each move down a row in a column. As students move up a row in a column to model 10 less than a number, they should begin relating how the digit in the tens place is decreasing with each move up a row. As students become more proficient with addition/subtraction of ten, instruction can extend to 100 more/ 100 less. In accordance with the TEKS, students also need to connect their findings through the use of properties of numbers and operations (i.e. Ten more than 234 is 244 because 234 + 10 = ___; 200 + 30 + 4 + 10 = ___; 200 + 30 + 10 + 4 = 200 + 40 + 4 = 244).

Students will begin identifying patterns in determining 10 or 100 more/less than a given number. Recognizing the change in the digits will reinforce tens and hundreds place value. This standard will reinforce place value in support of comparing and ordering whole numbers. 2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (<, >, or =)

This SE provides a foundation for 2.2D and builds upon 1.5C.

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Students will locate and name points on a number line (see 2.2E/F). Instruction needs to address that whole numbers identified on a number line represent the distance away from zero. This understanding will then be related to the use of the ruler and how the whole numbers identified on a ruler represent a measureable length (see 2.9D). In conjunction with 2.4B/C, instruction could extend the use of a number line in adding and subtracting two-digit numbers (i.e. 39 + ___ = 72).

Identifying whole numbers as distances from any given location can relate to the effective use of a ruler. This understanding will support the solving of problems involving length. Being able to represent whole number on a number line will support the comparing and ordering of numbers as larger numbers progress to the right and smaller numbers progress to the left of a number line. The understanding of whole numbers as distances from a given location will support the use of a number line as a strategy to add and subtract numbers. 2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (<, >, =) 2.9E determine a solution to a problem involving length, including estimating lengths

This SE has added number lines as a representation of distance (length). This allows connections to linear measurement in 2.9D.

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Course: Grade 2 Math Bundle 3: 2-Digit Addition and Subtraction (Strategies and Problem Solving)

Dates: October 10th-October 28th (15 days)

TEKS 2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations (algorithms will be introduced in Bundle 8) 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms (algorithms will be introduced in Bundle 8)(3-digit addition and subtraction will be introduced in Bundle 7) 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 (3-digit addition and subtraction will be introduced in Bundle 7) 2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

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4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary Addition Number sentence Properties of numbers Subtraction Term Difference Place value Strategies Sum Unknown Equation

Cognitive Complexity Verbs: add, subtract, use, solve, generate, represent Academic Vocabulary by Standard: 2.4B: addition, difference, place value, properties of numbers, subtraction, sum 2.4C: addition, difference, place value, strategies, subtraction, sum 2.4D: addition, difference, equation, number sentence, subtraction, sum 2.7C: addition, difference, number sentence, equation, subtraction, sum, term, unknown



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K.3C explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences 1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences

2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations


1.3A use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99 1.3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10

2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms


1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20

2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000





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Students will employ their understanding of place value and expanded notation to develop mental strategies to add multiple two-digit numbers. Properties of operations include the commutative, associative, and inverse properties. Although the teacher may model the names of the properties (i.e. commutative, associative, inverse, etc.), students will only be asked to employ the underlying concepts in order to solve addition and subtraction problems. (i.e. Commutative & Associative Property: 34 + 16 + 23 + 12 = ___ (30 + 4) + (10 + 6) + (20 + 3) + (10 + 2) = ___= (30 + 10 + 20 + 10) + (4 + 6 + 3 + 2) = 70 + 15 = 85) (i.e. Inverse Property: 62 – 58 = ___ 58 + ___ = 62; applying adding on, 59, 60, 61, 62; 62 – 58 = 4). Once students become fluent using the mental strategies, the traditional algorithm can be introduced relating the steps in the algorithm to the steps in the mental math strategies described above.

Adding multi-digit numbers based on place value and properties of operations is a fundamental skill in order to solve multi-step addition problems. 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

The limitations of this SE do not constrain the work with addition and subtraction in other SEs. Given the problem 24 + 55 + 36 + 45, students may decompose the addends based on place value, regroup, and combine using mental math. (20 + 50 + 30 + 40) + (4 + 6) + (5 + 5)= 140 + 10 + 10 = 160 Students may also use compatible numbers. (24 + 36) + (55 + 45) = 60 + 100 = 160


In conjunction with 2.4B, students will apply their strategies for addition and subtraction to solve real world problems. Instruction should include how the subtraction symbol represents distance (i.e.

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem.

The SE includes the addition and subtraction of three-digit numbers. Strategies may include properties of operations. For example, 432 + 241 may be thought of as:

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How far away is 3 from 11 on the number line in the following problem, 11 – 3 = ___?). This understanding of subtraction representing distance will lay the foundation for future learning of subtraction of integers (i.e. in the problem 11 – (-3) = 14, the number – 3 is 14 spaces away from 11). In adherence to the standard, students are required to solve multi-step word problems. Instruction should include samples of multiple step addition, subtraction, and a mixture of addition and subtraction problems. Students may need a visual to represent multiple-step understanding.

Whole Part Part Part

Word problems should include a variety of contexts: Joining: Sarah had 43 pencils. Juan gave her 18 more pencils. How many pencils does Sarah have now? Sarah had 25 pencils. Juan gave her some more pencils. Now Sarah has 43 pencils. How many pencils did Juan give her? Sarah had some pencils. Juan gave her 18 pencils. Now Sarah has a total of 43 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 43 pencils. She gave 18 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 43 pencils. She gave some to Juan. Now she only has 25 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave

* Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 – 18 = ___ is the same thing as 18 + ___ = 42).

(400 + 200) + (30 + 40) + (2 + 1) = 600 + 70 + 3 = 673 Fluency with this skill occurs in grade 3.

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18 to Juan. Now Sarah has 25 pencils left. How many pencils did Sarah have before? Comparing: Juan has 43 pencils and Sarah has25 pencils. How many more pencils does Juan have than Sarah? Sarah has 18 fewer pencils than Juan. If Sarah has 25 pencils, how many pencils does Juan have? Juan had 18 more pencils than Sarah. If Juan has 43 pencils, how many pencils does Sarah have? If Juan has 43 and Sarah has 25, how many more does Sarah need to have the same amount as Juan?


In adherence to the standard, students not only have to solve word problems that are provided to them, but they must also create their own story problems when given a number sentence. This standard will assess whether students understand the conceptual difference between addition and subtraction. Instruction should provide students opportunities to write story problems with multiple representations of various number sentences (i.e. 42 – 18 = ___; ___ = 42 – 18; 18 + ___ = 42; 18 + ___ + 6 = 42; ___ = 42 – 6 – 18; ___ = 42 – 18 + 4).

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem. * Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 – 18 = ___ is the same thing as 18 + ___ = 42).

This SE includes the addition and subtraction of three-digit numbers. Students must be provided with a mathematical number sentence in order to generate and then solve their problem situations. To build on 2.7C, the unknown may be any one of the terms.


In conjunction with 2.4, students continue to demonstrate their understanding of addition and subtraction with the appropriate number sentence. Instruction should vary the context of +/- type problems provided to students (see 2.4C for examples). In adherence to the standard, students should represent the

Relating addition and subtraction number sentences/equations supports a student’s ability to represent and solve addition and subtraction problems. 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and

When paired with 2.1C and 2.1D, the students are expected to represent problems with objects, manipulatives, diagrams, language, and number. Students may be expected to solve problems using number sense, mental math, and algorithms based on place value and properties of operations.

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same word problem with a variety of number sentences (i.e. 17 + 18 = ___; 18 + 17 = ___; ___ = 18 + 17; ___ = 17 + 18); (i.e. 42 – 16 = ___; ___ = 42 – 16; 16 + ___ = 42; 42 = ___ + 16).

subtraction of whole numbers within 1,000

For example, Jasmine has 87 books. She has some paperback books and 39 hardback books. How many paperback books does Jasmine have? Represent: 87 = { } + 39

Solve: 87 = 40 + 40 + 7 = 39 + (1 + 40 + 7) = 39 + 48

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Course: Grade 2 Math Bundle 4: Money Dates: October 31st- November 18th (15 days) TEKS

2.5A: determine the value of a collection of coins up to one dollar 2.5B: use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

ELPS

Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed Speaking 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3E: share information in cooperative learning interactions 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Cent symbol Decimal point Dollar sign Part Quarters Cents Dimes Nickels Pennies Whole Coins Dollar

Cognitive Complexity Verbs: determine, use Academic Vocabulary by Standard: 2.5A: coins, pennies, nickels, dimes, quarters, dollar, cents 2.5B: cent symbol, coins, dollar sign, decimal point, part, whole


Coins Hundreds Chart Part/Whole Mat Base 10 Blocks Place Value Chart Number Lines

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1.4C use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

2.5A: determine the value of a collection of coins up to one dollar

3.4C determine the value of a collection of coins and bills

1.4B write a number with the cent symbol to describe the value of a coin

2.5B: use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

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2.5A: determine the value of a collection of coins up to one dollar

Students are to apply their knowledge of skip counting (see 1.5B) to determine the value of a collection up to one dollar (i.e. skip count by twos to count a collection of pennies; skip count by fives to count a collection of nickels; skip count by tens to count a collection of dimes). As students become comfortable with determining the value of a collection of like coins, instruction should then address a mixture of unlike coins. Again, associating a child’s understanding of skip counting will allow them to add the value with ease (i.e. given 3 dimes, 4 nickels, and 6 pennies, students will skip count by tens to add the value of dimes 10, 20, 30, skip count by fives to add the value of the nickels 35, 40, 45, 50, and then skip count by twos to add the value of the pennies; 52, 54, 56). In adherence to the standard, students should solve problems involving monetary transactions.

* Students may not recognize the heads and/or tails side of a coin. * Students may not recognize non-traditional coins. * Students may confuse the size of the coin with its value (i.e. a nickel is worth more than a dime because it is larger in size).

This SE builds on K.4A and 1.4A, B, and C.

2.5B: use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

In conjunction with 2.5A, students will begin using the cent symbol or the dollar sign and decimal point to represent the value of a collection of coins. Instruction should address that money can be represented two ways (i.e. 42￠or $0.42) but cannot be represented using both symbols (i.e. $0.42￠). Instruction should address how the decimal point is used to separate the dollars (whole) from the cents (part).

Being able to symbolically represent the value of a collection of coins appropriately is critical in solving monetary transactions. 2.5A: determine the value of a collection of coins up to one dollar

Students are expected to use the notation for money rather than describe the use of that notation. To describe a set of coins with 4 dimes and 6 pennies, a student may write 46¢ or $0.46. Please note that 0.46¢ describes 46/100 of 1¢.

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Course: Grade 2 Math Bundle 5: Understanding Contextual Multiplication and Division

Dates: November 28th-December 16th (15 days)

TEKS 2.6A: model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined 2.6B: model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary Equivalent sets Repeated addition Repeated subtraction Separated

Cognitive Complexity Verbs: model, create, describe Academic Vocabulary by Standard: 2.6A: equivalent sets, repeated addition 2.6B: equivalent sets, repeated subtraction, separated


Counters Base 10 Blocks Hundreds Charts Money Number Lines

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2.6A: model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined

3.4D determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10 3.4E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts 3.4G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties 3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

2.6B: model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

3.4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally 3.4J determine a quotient using the relationship between multiplication and division 3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

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TEKS/Student Expectations Instructional Implications Distractor Factors Supporting Readiness Standards


2.6A: model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined

Students should be provided a variety of opportunities to model the joining of equal groups with objects (i.e. Using manipulatives a student can model how many wheels are on six tricycles). Instruction will not represent the multiplication situations with a multiplicative number sentence (i.e. 3 x 6 = 18). As outlined by the TEKS, students are to connect multiplicative situations to repeated addition. Therefore the recording of an addition number sentence would be appropriate (i.e. 3 + 3 + 3 + 3 + 3 + 3 = 18). In adherence to the standard, students should also create situations where repeated addition can be modeled.

This supporting standard develops the conceptual understanding of multiplication. The manipulation of objects into equal groups, the creation of multiplicative scenarios, and the verbal description of multiplicative situations provides the foundation for future problem solving. 3.4K solve one- step and two-step problems involving multiplication and division within 100 using strategies based on objects, pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

Given multiplication situations, students are expected to model and describe the situation. For example: There are 3 rows of chairs in the library. Each row has 5 chairs. How many chairs are in the library?

Three rows of 5 chairs represents 15 chairs. Students may also be expected to create multiplication situations. This SE lays the foundation for the development and mastery of multiplication facts in 3.4D.

2.6B: model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

Students should be provided a variety of opportunities to model the separating of a set of objects into equivalent groups (i.e. Using manipulatives, students model how many tricycles are needed using 18 wheels). Instruction will not represent the division situations with a division number sentence (i.e. 18 ÷ 3 = 6). As outlined by the TEKS, students are to connect divisional situations to repeated subtraction. Therefore the recording of a subtraction number sentence would be appropriate (i.e. 18 – 3 –

This supporting standard develops the students’ conceptual understanding of division which they will need in order to understand, appropriately represent, and solve division problems. 3.5B represent and solve one-and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

Given division situations, students are expected to model and describe the situations. For example: There are 24 chairs in Ms. Garcia’s room. She separated the chairs equally into 4 rows. How many chairs did she place in each row?

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3 – 3 – 3 – 3 – 3 = 0). Divisional situations should be limited to those that yield equal groupings/shares (no remainders). In adherence to the standard, students should also create situations where repeated subtraction will be modeled.

24 chairs separated into 4 rows represents 6 chairs in each row. Students may also be expected to create division situations. This lays the foundation for the development and mastery of division facts in 3.4F, H, and J.

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Course: Grade 2 Math Bundle 6: Data Analysis

Dates: January 2nd- January 12th (9 days)

TEKS 2.10A: explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category 2.10B: organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more 2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one 2.10D: draw conclusions and make predictions from information in a graph

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Addition Data points Horizontal Labels Subtraction Bar graph Difference Information Length Sum Category Graph title Interval Pictograph Vertical Data

Cognitive Complexity Verbs: explain, organize, use, write, solve, draw conclusions, make predictions Academic Vocabulary by Standard: 2.10A: bar graph, category, data, data points, length, pictograph 2.10B: bar graph, categories, data, graph title, interval, labels, pictograph 2.10C: addition, bar graph, horizontal, vertical, data, difference, information, interval, pictograph, subtraction, sum 2.10D: bar graph, horizontal, information, pictograph, vertical


Counters Snap Cubes Color Tiles Chart Paper Graph Paper

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2.10A: explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category

K.8B use data to create real-object and picture graphs 1.8B use data to create picture and bar-type graphs

2.10B: organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more

3.8A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals 4.9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals 4.9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

K.8C draw conclusions from real-object and picture graphs 1.8C draw conclusions and generate and answer questions using information from picture and bar-type graphs

2.10D: draw conclusions and make predictions from information in a graph

3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals 4.9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

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2.10A: explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category

According to the TEKS, students will organize data (i.e. results of a poll of 2nd grade students’ favorite color) in a bar graph or pictograph. As students begin organizing the data, they need to understand the difference between category (i.e. red, green, blue, etc.) and data points (i.e. number of students that selected a particular category). The length of bar graph or the number of pictures in a pictograph identifies the number of data points for a particular category.

Understanding the length of the bar graph or the number of pictures in a pictograph represents the number of data points for a given category will support a student in accurately solving addition/subtraction problems and summarization of data. 2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

Students are expected to explain their construction of a pictograph or a bar graph. When paired with 2.1A, students may be expected to collect and sort their own data before organizing it.

2.10B: organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more

It is imperative for students to generate a question before a unit of study on data (i.e. What types of flowers grow in my Grandmother’s garden?). Instruction should encourage students to extend beyond two categories (i.e. roses, carnations, and daffodils), yet restrict the sorting to within four categories (i.e. sorting by the different color of flowers may yield too many categories). Students are then to collect their own data as this will make more of a personal connection when interpreting the data. Students will organize their data through the use of a pictograph (one picture/ icon represents one or more than one piece of data) or bar graph (intervals of one or more). Ensure that students title and label their models/ representations.

Having students collect, sort, and organize their own data allows students to be able to understand how to solve various problems based on the data. Understanding how to create and interpret data using pictographs and bar graphs will evolve into the use of frequency tables and dot plots in future grades. 2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

This SE builds upon K.8A and 1.8A. The number of categories has been constrained to 4. Intervals may be one or more.

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2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

As students organize their data into pictographs and/or bar graphs (see 2.10B), instruction should then lead students to creating their own questions (i.e. How many more daffodils did my grandmother have in her garden than roses? How many roses and carnations are there in Grandma’s garden?). Designing appropriate questions that relate to the data is an informal way to assess whether students understand the information represented in the graphs. Students could then exchange their graphs and ask fellow classmates to answer their self-generated questions. Note that in the difference between 2.10B and 2.10C; students must organize data with interval graphs of one or more but the writing and solving of problems is limited to graphs with intervals of one only.

* Students may misinterpret pictographs in which each picture represents a value other than one. * Students may misread bar graphs that have scaled intervals. * When representing the same set of data on the two types of graphs, students may interpret the data as different because they are represented with different graphs. * When representing the same set of data vertically and horizontally, students may interpret the data as different because of the difference in the visual representations. * Students may apply the use of “key words” instead of understanding the context of the problem.

Students are now expected to write problems involving addition and subtraction using data represented within the stated graphs with limitations of intervals of one.

2.10D: draw conclusions and make predictions from information in a graph

According to the TEKS, students need to collect, organize, and display their own data. Personalizing such activities will allow students to make more sense of the data and summarize more appropriately. Instruction needs to include multiple categories (i.e. extend survey question, “Do you like cats or dogs?” to “What is your favorite animal?”). In accordance with the standard, data should be represented on a pictograph or bar graph. Vertical and horizontal representations should be included. Pictographs should include symbolism that does not

Drawing conclusions and making predictions from information in a graph will allow students to write and solve associated word problems more effectively. 2.10C: write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

Based on 2.10A and 2.10B, information may be represented with pictographs and bar graphs.

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represent one-to-one correspondence (i.e. A smiley face represents 4 people) and portion representations (i.e. a picture of half a smiley face yields 2 people). Bar graphs include scaled intervals (i.e. information on the x- or y-axis skip count by tens). Extend instruction to include representing the same data set in both types of displays to compare. Summarization of data should also include being able to determine the total amount of data collected by viewing a graph (i.e. The sum of each bar graph length will yield the total number of data pieces).

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Course: Grade 2 Math Bundle 7: 3-Digit Addition and Subtraction (Strategies and Problem Solving)

Dates: January 17th-February 3rd (14 days)

TEKS 2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations (algorithms will be introduced in Bundle 8) 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms (algorithms will be introduced in Bundle 8) 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

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Vocabulary





52














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2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including

In conjunction with 2.4B, students will apply their strategies for addition and subtraction to solve real world problems. Instruction should include how the



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algorithms subtraction symbol represents distance (i.e. How far away is 3 from 11 on the number line in the following problem, 11 – 3 = ___?). This understanding of subtraction representing distance will lay the foundation for future learning of subtraction of integers (i.e. in the problem 11 – (-3) = 14, the number – 3 is 14 spaces away from 11). In adherence to the standard, students are required to solve multi-step word problems. Instruction should include samples of multiple step addition, subtraction, and a mixture of addition and subtraction problems. Students may need a visual to represent multiple-step understanding.


Word problems should include a variety of contexts: Joining: Sarah had 43 pencils. Juan gave her 18 more pencils. How many pencils does Sarah have now? Sarah had 25 pencils. Juan gave her some more pencils. Now Sarah has 43 pencils. How many pencils did Juan give her? Sarah had some pencils. Juan gave her 18 pencils. Now Sarah has a total of 43 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 43 pencils. She gave 18 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 43 pencils. She gave some to Juan. Now she only



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has 25 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 18 to Juan. Now Sarah has 25 pencils left. How many pencils did Sarah have before? Comparing: Juan has 43 pencils and Sarah has25 pencils. How many more pencils does Juan have than Sarah? Sarah has 18 fewer pencils than Juan. If Sarah has 25 pencils, how many pencils does Juan have? Juan had 18 more pencils than Sarah. If Juan has 43 pencils, how many pencils does Sarah have? If Juan has 43 and Sarah has 25, how many more does Sarah need to have the same amount as Juan?






In conjunction with 2.4, students continue to demonstrate their understanding of addition and subtraction with the appropriate number sentence. Instruction should vary the context of +/- type problems provided to students (see 2.4C for examples).

Relating addition and subtraction number sentences/equations supports a student’s ability to represent and solve addition and subtraction problems. 2.4D: generate and solve problem situations for a given

When paired with 2.1C and 2.1D, the students are expected to represent problems with objects, manipulatives, diagrams, language, and number. Students may be expected to solve problems using number sense, mental math, and algorithms

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In adherence to the standard, students should represent the same word problem with a variety of number sentences (i.e. 17 + 18 = ___; 18 + 17 = ___; ___ = 18 + 17; ___ = 17 + 18); (i.e. 42 – 16 = ___; ___ = 42 – 16; 16 + ___ = 42; 42 = ___ + 16).

mathematical number sentence involving addition and subtraction of whole numbers within 1,000

based on place value and properties of operations. For example, Jasmine has 87 books. She has some paperback books and 39 hardback books. How many paperback books does Jasmine have? Represent: 87 = { } + 39

Solve: 87 = 40 + 40 + 7 = 39 + (1 + 40 + 7) = 39 + 48

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Course: Grade 2 Math Bundle 8: Exploring the Addition and Subtraction Standard Algorithms and Problem Solving

Dates: February 6th- February 17th (10 days)

TEKS 2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 2.7C: represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials

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Vocabulary





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2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including

In conjunction with 2.4B, students will apply their strategies for addition and subtraction to solve real world problems. Instruction should include how the



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algorithms subtraction symbol represents distance (i.e. How far away is 3 from 11 on the number line in the following problem, 11 – 3 = ___?). This understanding of subtraction representing distance will lay the foundation for future learning of subtraction of integers (i.e. in the problem 11 – (-3) = 14, the number – 3 is 14 spaces away from 11). In adherence to the standard, students are required to solve multi-step word problems. Instruction should include samples of multiple step addition, subtraction, and a mixture of addition and subtraction problems. Students may need a visual to represent multiple-step understanding.


Word problems should include a variety of contexts: Joining: Sarah had 43 pencils. Juan gave her 18 more pencils. How many pencils does Sarah have now? Sarah had 25 pencils. Juan gave her some more pencils. Now Sarah has 43 pencils. How many pencils did Juan give her? Sarah had some pencils. Juan gave her 18 pencils. Now Sarah has a total of 43 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 43 pencils. She gave 18 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 43 pencils. She gave some to Juan. Now she only



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has 25 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 18 to Juan. Now Sarah has 25 pencils left. How many pencils did Sarah have before? Comparing: Juan has 43 pencils and Sarah has25 pencils. How many more pencils does Juan have than Sarah? Sarah has 18 fewer pencils than Juan. If Sarah has 25 pencils, how many pencils does Juan have? Juan had 18 more pencils than Sarah. If Juan has 43 pencils, how many pencils does Sarah have? If Juan has 43 and Sarah has 25, how many more does Sarah need to have the same amount as Juan?






In conjunction with 2.4, students continue to demonstrate their understanding of addition and subtraction with the appropriate number sentence. Instruction should vary the context of +/- type problems provided to students (see 2.4C for examples).

Relating addition and subtraction number sentences/equations supports a student’s ability to represent and solve addition and subtraction problems. 2.4D: generate and solve problem situations for a given

When paired with 2.1C and 2.1D, the students are expected to represent problems with objects, manipulatives, diagrams, language, and number. Students may be expected to solve problems using number sense, mental math, and algorithms

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In adherence to the standard, students should represent the same word problem with a variety of number sentences (i.e. 17 + 18 = ___; 18 + 17 = ___; ___ = 18 + 17; ___ = 17 + 18); (i.e. 42 – 16 = ___; ___ = 42 – 16; 16 + ___ = 42; 42 = ___ + 16).

mathematical number sentence involving addition and subtraction of whole numbers within 1,000

based on place value and properties of operations. For example, Jasmine has 87 books. She has some paperback books and 39 hardback books. How many paperback books does Jasmine have? Represent: 87 = { } + 39

Solve: 87 = 40 + 40 + 7 = 39 + (1 + 40 + 7) = 39 + 48

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Course: Grade 2 Math Bundle 9: Geometry

Dates: February 21st – March 10th (14 days)

TEKS 2.8A: create two-dimensional shapes based on given attributes, including number of sides and vertices 2.8B: classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language 2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices 2.8D: compose two-dimensional shapes and three-dimensional solids with given properties or attributes 2.8E: decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

ELPS Learning Strategies 1B: monitor oral and written language production and employ self-corrective techniques or other resources 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E: share information in cooperative learning interactions Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Attributes Geometric parts Pentagon Rhombus Three-dimensional Cone Hendecagon Polygon Shape Trapezoid Cube Heptagon Properties Sides Triangle Cylinder Hexagon Quadrilateral Solid Triangular prism Dodecagon Nonagon Rectangle Sphere Two-dimensional Edges Octagon Rectangular prism Square Vertex/vertices Faces Parallelogram

Cognitive Complexity Verbs: create, classify, sort, identify, compose, decompose Academic Vocabulary by Standard: 2.8A: attributes, polygon, shape, sides, two-dimensional, vertex/vertices 2.8B: attributes, faces, edges, vertex/vertices, three-dimensional, solid, sphere, cone, cylinder, rectangular prism, cube (as special rectangular prism), triangular prism 2.8C: attributes, sides, vertex/ vertices, polygons, triangle, quadrilaterals, rectangle, square, rhombus, parallelogram, trapezoid, pentagon, hexagon, heptagon, octagon, nonagon, decagon, hendecagon, dodecagon 2.8D: attributes, edges, faces, sides, vertex/vertices, polygons, properties, shapes, solids, three-dimensional, two-dimensional 2.8E: geometric parts, polygon, shape, two-dimensional


AngLegs Pattern Blocks Geoboards Translucent Geometric Shapes Power Polygons Geometric Solids

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K.6A identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles K.6D identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably 1.6C create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 1.6D identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

2.8A: create two-dimensional shapes based on given attributes, including number of sides and vertices

3.6B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories 4.6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines 4.6B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure 4.6C apply knowledge of right angles to identify acute, right, and obtuse triangles

K.6E classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

2.8B: classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

3.6A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

K.6E classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size 1.6A classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language

2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

3.6A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language 4.6D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

K.6F create two-dimensional shapes using a variety of materials and drawings 1.6F compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible

2.8D: compose two-dimensional shapes and three-dimensional solids with given properties or attributes

2.8E: decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

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2.8A: create two-dimensional shapes based on given attributes, including number of sides and vertices

Students are provided with a variety of materials (i.e. toothpicks, straws, string, marshmallows, clay, etc.) and a description of a two-dimensional shape (i.e. polygon with five sides and five vertices). Students are to use the materials to build the shape or arrange the materials to create the shape based on the give attributes and associate the materials to the appropriate geometric attribute (i.e. The five marshmallows represent the five vertices and the five toothpicks represent the five sides of the pentagon). Instruction should extend to modify the rectangle to make it a square and explain how the attributes/ properties of the two shapes were similar yet different.

Creating two-dimensional shapes given the number of sides and vertices allows students to focus on the geometric attributes of a figure. This attention to specific attributes will support the classification and sorting of various polygons. 2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

Students are expected to create shapes based on given attributes such as a triangle when given the attributes of exactly 3 sides and exactly 3 vertices.

2.8B: classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

Students must be given a variety of three-dimensional solids to sort based on their attributes (i.e. number of edges, number of vertices, number/ types of faces, etc.). In adherence to the standard, solids are limited to prisms and do not include pyramids. It is essential for student to recognize that a cube is a rectangular prism; it is a special rectangular prism that has all edges equal in length. Instruction should relate how three-dimensional figures are comprised of two-dimensional shapes (i.e. six rectangles are put together to make a rectangular prism).

* Students may interchange the term side referencing two-dimensional shapes and edge referencing three-dimensional shapes. * Students may count the common vertices of a three-dimensional figure twice as they view each face independently. * Students may not view a square as a rectangle or a cube as a rectangular prism.

Formal geometric language includes terms such as vertex, edge, and face. Students are expected to classify solids. The comparison of similarities and differences among solids supports classification and sorting.

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2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

Students must be given a variety of two-dimensional shapes to sort based on their attributes. In adherence to the standard, students need exposure to polygons up to 12 sides (i.e. triangles, quadrilaterals, pentagons, hexagons, heptagons, octagon, nonagon, decagon, etc.). Students need to be exposed to both regular (i.e. pentagon with all five sides equal length) and irregular (i.e. chevron shaped pentagon where all sides are not of equal length) two-dimensional figures.

* Students may interchange the term side referencing two-dimensional shapes and edge referencing a three-dimensional shape. * Students may not view a square as a rectangle.

Students are expected to classify polygons. The comparison of similarities and differences among polygons supports classification. Classifying a polygon includes naming the polygon, such as a 10-sided polygon as a decagon.

2.8D: compose two-dimensional shapes and three-dimensional solids with given properties or attributes

Students are provided with a variety of materials (i.e. toothpicks, straws, string, marshmallows, clay, etc.) and a description outlining properties and/ or attributes for a given figure (i.e. a solid with 8 vertices, 6 faces, and 12 edges which are not all of equal length). Students are to use the materials to build the figure based on the given attributes and associate the materials used to the appropriate geometric attribute (i.e. the 8 balls of clay on each end represent the eight vertices and the 12 straws represent the 12 edges of my rectangular prism. However, I had to cut the straws to be different in length so that it would not represent a cube).

Creating two- and three-dimensional shapes given attributes (i.e. the number of sides and vertices) and properties (i.e. all sides are of different lengths) requires students to focus on the geometric attributes of a figure. This attention to specific attributes and properties will support the classification and sorting of various figures. 2.8B: classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language 2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

Students are expected to compose 2D shapes and 3D solids such as building a rectangle out of square-inch tiles or building a rectangular prism out of unit cubes. Students are expected to compose shapes when given properties. For example: Compose a figure with 6 sides and 6 vertices using 2 shapes.

2.8E: decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in

As students begin to recognize and describe the attributes of given two-dimensional shapes,

Decomposing shapes into other polygons will support the classification and sorting of two-

An example of how a student might decompose a 2D shape has been provided.

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half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

instruction will lead to more spatial reasoning development. Students will be given a targeted two-dimensional shape (i.e. a trapezoid) and asked to decompose the figure into different smaller geometric parts (i.e. a rectangle and one triangle). Encourage students to partition shapes in different ways.

dimensional figures. The student will have to focus on the various attributes to identify the resulting geometric parts. 2.8C: classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

In grade 2, the focus on decomposing shapes complements the work with fractional parts of a whole in 2.3A, B, and D.

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Course: Grade 2 Math Bundle 10: Fractions

Dates: March 20th- April 7th (15 days)

TEKS 2.3A: partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words 2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part 2.3C: use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole 2.3D: identify examples and non-examples of halves, fourths, and eighths

ELPS Learning Strategies 1B: monitor oral and written language production and employ self-corrective techniques or other resources 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language Speaking 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

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Vocabulary

Unit Vocabulary Eighths Examples Fraction Non-examples Equal parts Fourths Halves Whole

Cognitive Complexity Verbs: partition, explain, use, recognize, identify Academic Vocabulary by Standard: 2.3A: equal parts, halves, fourths, eighths, fractional units, whole 2.3B: fraction, fractional parts, whole 2.3C: equal parts, fractional parts, whole 2.3D: equal parts, examples, non-examples, fractional units, halves, fourths, eighths, whole


Geoboards Fraction Circles (unlabeled) Translucent Geometric Shapes

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2.3A: partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

2.3C: use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

2.3D: identify examples and non-examples of halves, fourths, and eighths

3.3A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

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2.3A: partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words

As identified by the cognitive expectation of this standard, students should be provided with a whole object and asked to partition it into two, four, and/or eight equal parts. Students should then be able to describe the equal parts in words (i.e. halves, fourths, and eighths). Instruction will not extend to the symbolic (i.e. ½. ¼. 1/8) until grade 3. Encourage students to find more than one way to divide a given shape into equal parts (i.e. a square can be divided in two equal parts vertically, horizontally, or diagonally). This will develop a student’s understanding of how it is possible for various shapes to represent the same fractional part (i.e. the rectangle formed from dividing the square vertically represents one-half and so does the triangle formed when the same square was divided diagonally). The use of geoboards will support the trial and error process of finding more than one way and comparing the amount of area represented in each fractional part regardless of the shape created.

This supporting standard develops the conceptual understanding of fractional parts of a whole. Being able to physically partition objects into equal parts in various ways will allow students to observe how the size of the parts vary depending on the number of equal parts. 2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

Students are to partition objects using previously partitioned objects. Objects may be one- or two-dimensional in form, such as strips, lines, regular polygons, or circles. Emphasis should be on the naming of fractions with words rather than fraction notation a/b. The words may include names such as “one half” or “three fourths.” Students are not expected to note the relationship between the number of fourths that equal one half, etc.

2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

In conjunction with 2.3A, as students are partitioning whole objects into 2,4, and 8 equal parts, they need to recognize that the more parts an object is divided into, the smaller the parts become; the fewer parts an object is divided into, the larger the parts become. Instruction should provide real world examples to build conceptual understanding (i.e. Would you rather share a candy bar with two friends or four? Would you rather

* Students may not understand that the more times you divide a whole object into parts, the smaller the parts become. * Students may think that 1/8 is larger than 1/6 because 8 is bigger than 6. * Students may not understand that the fractional parts must be equal.

When paired with 2.1A or 2.1G, students may be expected to explain this foundational fraction concept in a real-life situation. For example, Juan asked for one-half of a medium pizza. Callie asked for one-eighth of a medium pizza. Who is receiving the greater amount of pizza? Why?

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have a slice of a pizza that was cut into eight equal parts or ten equal parts?).

2.3C: use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole

All fraction lessons should begin with identifying how many parts it takes to equal one whole. This first step will alleviate the misconception of whether a fractional representation is greater than or less than one whole. In adherence to this standard, students will use manipulatives to represent fractional parts beyond one whole. Students identify that the whole is made up of four equal parts and they will be counting in fourths. Students must count each shaded part as one-fourth, two-fourths, three-fourths, four-fourths, five-fourths, etc. Students relate that it takes four parts to represent one whole. Thus, five-fourths can also be called one and one-fourth. Instruction is limited to word use only (i.e. one-fourth; two-fourths, etc.) not the symbolic representation (i.e. 5/4 or 1 ¼).

Recognizing how many parts it takes to equal one whole will direct the student to focus on the size of the parts. The size of the parts will allow the learner to more accurately compare fractions. Counting fractional parts beyond one whole supports the concrete understanding of improper fractions and mixed numbers being equivalent (i.e. “Five-fourths” is the same as “one and one-fourth”). 2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

Counting may include a sequence of fractional names such as “one fourth,” “two fourths,” “three fourths,” “four fourths,” “five fourths,” or “one and one fourth.” Using a sentence such as “four fourths equals one whole” would indicate recognition of how many parts it takes to equal one whole.

2.3D: identify examples and non-examples of halves, fourths, and eighths

In conjunction with 2.3A, as students are partitioning figures into 2/4/8 equal parts and describe them as halves/fourths/ eighths, students should recognize examples (i.e. Regular and irregular shapes divided equally) and non-examples of such partitions (i.e. Whole objects divided unequally). With the use of geoboards, students would be able to verify examples of halves/fourths/eighths by comparing the amount of area in each part.

Identifying examples and non-examples of fractional parts of the same whole will support student understanding of the part-to-whole relationship and the size of the parts. This knowledge will provide the foundation for being able to visually compare two fractions and/or concretely represent equivalent fractions. 2.3B: explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

Non-examples allow students to justify their thinking related to halves, fourths, and eighths. To build a foundation for 3.6E, examples of halves, fourths, and eighths may be shown that have equal areas but do not have congruent parts.

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Course: Grade 2 Math Bundle 11: Measurement

Dates: April 10th- May 5th (18 days)

TEKS 2.9A: find the length of objects using concrete models for standard units of length 2.9B: describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object 2.9C: represent whole numbers as distances from any given location on a number line 2.9D: determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes 2.9E: determine a solution to a problem involving length, including estimating lengths 2.9F: use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit 2.9G: read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1B: monitor oral and written language production and employ self-corrective techniques or other resources 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3E: share information in cooperative learning interactions 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

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Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary a.m. Distance Length Minute hand Square units About Estimation Location Number line Standard units Analog clock Feet Marked unit Overlaps Time Approximately Gaps Measuring tape p.m. Unit of measure Area Hour Meter stick Place value Whole numbers Centimeters Hour hand Meters Ruler Yards Digit Inches Minute Size of unit Yardstick Digital clock Inverse relationship

Cognitive Complexity Verbs: find, use, describe, represent, determine, read, write, distinguish Academic Vocabulary by Standard: 2.9A: length, standard units, centimeters, meters, inches, feet, yards 2.9B: inverse relationship, length, size of unit, unit of measure 2.9C: distance, location, number line, place value, whole numbers 2.9D: length, marked unit, measuring tape, meter stick, ruler, yardstick 2.9E: estimation, length, about, approximately 2.9F: area, gaps, overlaps, about, approximately, square units 2.9G: a.m., p.m., analog clock, digit, digital clock, hour, hour hand, minute, minute hand, number line, time


Rulers Measuring Tape Yard Sticks Meter Sticks Color Tiles (inch) Centimeter Cubes Clocks Number Lines

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1.7B illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other 1.7D describe a length to the nearest whole unit using a number and a unit

2.9A: find the length of objects using concrete models for standard units of length

4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

1.7C measure the same object/distance with units of two different lengths and describe how and why the measurements differ

2.9B: describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object



3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line

K.7A give an example of a measurable attribute of a given object, including length, capacity, and weight 1.7A use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement

2.9D: determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes


2.9E: determine a solution to a problem involving length, including estimating lengths

3.7B determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems 4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

2.9F: use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit

3.6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row 3.6D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area 3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

1.7E tell time to the hour and half hour using analog and digital clocks

2.9G: read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.

3.7C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes 4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

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2.9A: find the length of objects using concrete models for standard units of length

The use of non-standard units of measure (i.e. Teddy bear counters, paper clips, index cards, etc.) will be restricted to only models that represent an approximate standard unit of length (i.e. a unit cube represent a centimeter, a color tile represents and inch, a ruler represents a foot, etc.). As non-standard units of measure will also be used to determine area (2.9F), it will be critical to identify that only the length of one of the sides of the manipulative will be used to measure length, not the entire object (i.e. When measuring in inches, we will only be using the length of one of the sides of a color tile to determine length). Students will measure lengths of various objects and record the measurements in standard units of measure (i.e. The length of a notebook was approximately 11 color tiles in length measuring about 11 inches). It is imperative that instruction allow plenty of time for students to engage in the use of concrete models representing a standard unit of measure as a mental image of the length of a centimeter, inch, foot, yard, etc. will lead to more educated estimations and reasonableness of length (i.e. See 2.9E).

This supporting standard develops the conceptual understanding that perimeter is the measurement of length. The use of non-standard units of measure (concrete objects) to measure length will develop a visual benchmark of various lengths which will support a student’s ability to estimate lengths more appropriately. 2.9E: determine a solution to a problem involving length, including estimating lengths

The concrete models should represent a standard unit of length such as the edges of inch tiles or centimeter cubes.

2.9B: describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object

Students should measure a given object with more than one unit of measure (i.e. measure the length of an index card using unit cubes and color tiles). In conjunction with 2.9A, students record both measurements in standard units of measure (i.e. 5 color tiles=5 inches, 15 unit cubes=15 centimeters). Students need to justify how it is possible to have two different measurement recordings for the same object (i.e. the length of the object was measured with different measurement tools). Instruction is to lead to the discovery that the longer the unit of measure, the fewer units of measure is needed; the shorter the unit of measure, the more units of measure is needed. This concept leads to future understanding of how an object measuring two yards in length is not shorter than an object measuring 6 feet in length.

Measuring the length of objects with a variety of concrete objects will support the understanding that length of objects can be measured in various units. This supporting standard will allow the learner to experience how the shorter the unit of measure, the more units needed to measure the length; the longer the unit of measure, the fewer units needed to measure the length. As students begin moving to measuring with a ruler, this non-standard unit

A student is expected to provide a description such as “the longer the unit, the fewer needed and the shorter the unit, the more needed to measure length.”

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of measurement experience will support how objects can be measured in centimeters and inches and the inverse relationship between the size of the units and the number of units needed to equal the length of an object. 2.9E: determine a solution to a problem involving length, including estimating lengths


Students will locate and name points on a number line (see 2.2E/F). Instruction needs to address that whole numbers identified on a number line represent the distance away from zero. This understanding will then be related to the use of the ruler and how the whole numbers identified on a ruler represent a measureable length (see 2.9D). In conjunction with 2.4B/C, instruction could extend the use of a number line in adding and subtracting two-digit numbers (i.e. 39 + ___ = 72).

Identifying whole numbers as distances from any given location can relate to the effective use of a ruler. This understanding will support the solving of problems involving length. Being able to represent whole number on a number line will support the comparing and ordering of numbers as larger numbers progress to the right and smaller numbers progress to the left of a number line. The understanding of whole numbers as distances from a given location will support the use of a number line as a strategy to add and subtract numbers. 2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (<, >, =) 2.9E determine a solution to a problem involving length, including estimating lengths

This SE has added number lines as a representation of distance (length). This allows connections of linear measurement in 2.9D.

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2.9D: determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes

This standard begins the transition from the use of concrete objects to measure length to the use of a formal measurement tool. Through the lens of the number line, students will begin associating the number line to the representation of various measurement tools (i.e. the whole numbers represented on a ruler). In conjunction with 2.9A, students can begin comparing the size of the concrete object they used to measure the length to the standard measuring tool (i.e. align 12 color tiles next to a ruler to demonstrate how 12 inches equals one foot). Students will measure the lengths of various objects using a variety of standard measurement tools (i.e. ruler, yard stick, meter stick, measuring tape). In adherence to the standard, students will only measure to the nearest whole number.

Hands-on experiences measuring the length of objects with a variety of measurement tools will be essential for students to estimate length and solve problems involving length to include perimeter. 2.9E: determine a solution to a problem involving length, including estimating lengths

Students are expected to use standard units of length and measure to the nearest whole unit such as an inch or a foot.

2.9E: determine a solution to a problem involving length, including estimating lengths

Instruction should provide a variety of problem situations involving length. Vary the context of the measurement problems (i.e. how many centimeters long is your pencil? If by sharpening your pencil you lost 2 centimeters of length, how long would the newly sharpened pencil be? How many inches longer is your notebook than your pencil? If you taped two pieces of paper together, how long would the new piece of paper be?). In adherence to the standard, word problems should include estimations as well, such as estimating the length of your eraser in centimeters. It is essential that students have a mental visual image of each of the standard units of measure in order to accurately estimate (i.e. I know a unit cube is about a centimeter and it looks like my eraser would be about 2 of those unit cubes; I estimate the length of my eraser to be 2 centimeters). Instruction should also include measuring with a measurement tool that does not start at zero (i.e. using your broken ruler, measure the length of your pencil).

* Students may not align the zero marking of the ruler appropriately. * Students may inaccurately read the length of an object being measured with a tool not aligned at the zero marking. * Students may think that an object measuring 12 inches in length is longer than an object measuring one foot because 12 is bigger than 1. * Students may not estimate a measurement reasonably because they do not have a good understanding of the size of various measures.

This is the first introduction to estimation in the TEKS outside of the mathematical process standards.

2.9F: use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit

Students will use square units (i.e. unit cubes, color tiles, sticky note pads, etc.) to determine the area of various rectangles. As non-standard units of measure have also been used to determine the length of objects (see 2.9A), it will be critical to identify that only the length of one of the sides of the manipulative was used to determine the length of an object. To determine area, we use the entire object (i.e. when measuring length, draw a line along one of the sides to visually

Hands-on experiences covering rectangles with square units with no gaps or overlaps develop the concrete understanding of area. The use of square units to cover the region of a rectangle supports the future understanding of how area is

The 2D figure has been constrained to rectangles, which includes squares. The concrete models should be square units, and the measurement should be described

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demonstrate that we only use this component of the measuring tool to determine length; when measuring area, outline and shade in the area of the square unit). As students begin to measure the area of various rectangles, they need to understand the amount of space inside the object is what is to be measured, the unit of measure must be consistent (i.e. unit cubes and color tiles cannot be mixed to cover the area of an object), their findings accordingly (i.e. the area of the index card is about 24 color tiles. The amount of space inside of the sticky note pad measures a little more than 20 unit cubes; approximately 88 color tiles cover my notebook).

reflected in square units. 3.6C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

using square units such as “24 square units.”

2.9G: read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.

Relate the clock to a circular, closed number line (see 2.2E/F). Create a number line identifying the whole numbers 0-12. Demonstrate how to connect both ends of the number line to create a circular number line referencing how the hour numerals on the clocks relate to those on a number line. Extend the use of the closed number line to include the minute increments. Instruction should relate the hour and minute hands from the analog clock to the digits represented on a digital clock. Clarify that the use of the colon (:) on the digital clock is to separate the hours (whole) from the minutes (part). Instruction should include discussions about how our day is divided into two equal parts (a.m. and p.m.). Activities that happen from midnight until noon are considered to occur in the a.m. and activities that happen from noon until midnight are considered to occur in the p.m. Creating a timeline of classroom activities with the appropriate a.m. /p.m. recordings may support this understanding.

Activity Time Reading 8:40 a.m.-9:55 a.m. Social Studies 9:55 a.m.- 10:40 a.m. Library 10:45 a.m.-11:30 a.m. Lunch 11:35 a.m.-12:25 p.m. Math 12:30 p.m.-1:30 p.m. Science 1:30 p.m.-2:30 p.m.

* Students may confuse the hour and minute hand. *Students may not be able to accurately read the hour hand as it falls between two hour points. * Students may be able to read time accurately but struggle when asked to represent a given time on a clock. * Students may think that activities that happen in the day time are a.m. and activities that happen in the night time are p.m. activities * Students may confuse 12:00 a.m. and 12:00 p.m.

This SE provides a foundation for solving problems involving time in 3.7C.

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Course: Grade 2 Math Bundle 12: Personal Financial Literacy

Dates: May 8th-May 19th (10 days)

TEKS 2.11A: calculate how money saved can accumulate into a larger amount over time 2.11B: explain that saving is an alternative to spending 2.11C: distinguish between a deposit and a withdrawal 2.11D: identify examples of borrowing and distinguish between responsible and irresponsible borrowing 2.11E: identify examples of lending and use concepts of benefits and costs to evaluate lending decisions 2.11F: differentiate between producers and consumers and calculate the cost to produce a simple item

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

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Vocabulary

Unit Vocabulary Benefits Cost Lending Responsible Spending Borrow Deposit Money saved Saving Withdrawal Consumers Irresponsible Producers

Cognitive Complexity Verbs: calculate, explain, distinguish, identify, use, evaluate, differentiate Academic Vocabulary by Standard: 2.11A: money saved 2.11B: saving, spending 2.11C: deposit, withdrawal 2.11D: borrow, irresponsible, responsible 2.11E: benefits, costs, lending 2.11F: consumers, cost, producers

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1.9C distinguish between spending and saving 2.11A: calculate how money saved can accumulate into a larger amount over time

3.9E list reasons to save and explain the benefit of a savings plan, including for college 4.10C compare the advantages and disadvantages of various savings options

2.11B: explain that saving is an alternative to spending 3.9C identify the costs and benefits of planned and unplanned spending decisions

2.11C: distinguish between a deposit and a withdrawal 4.10D describe how to allocate a weekly allowance among spending; saving, including for college; and sharing

2.11D: identify examples of borrowing and distinguish between responsible and irresponsible borrowing

3.9D explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest 4.10E describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending

2.11E: identify examples of lending and use concepts of benefits and costs to evaluate lending decisions

2.11F: differentiate between producers and consumers and calculate the cost to produce a simple item

3.9B describe the relationship between the availability or scarcity of resources and how that impacts cost 4.10B calculate profit in a given situation.

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2.11A: calculate how money saved can accumulate into a larger amount over time

Instruction should include discussions about how saving money over a period of time can yield you a larger amount of money. Providing real world second grade examples of savings accumulation will allow students to relate to the state expectation (i.e. Saving your positive behavior tickets will allow you to buy a more expensive prize from the class store). Perhaps, story problems involving real world situations of how money can be saved over a period of time could be incorporated into the Number and Operations strand (see 2.4C).

Calculating how savings accumulates larger amounts over time will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

These calculations should not include interest. This SE builds to 3.9E.

2.11B: explain that saving is an alternative to spending

Students will need to distinguish between spending money (on either wants or needs) and saving money (for either wants or needs). Providing real world second grade examples of student spending versus saving will allow students to relate to the state expectation (i.e. spending a student’s weekly allowance on video arcade games versus saving his/her money to purchase a video game that can be played at home over and over). Story problems involving real world situations of money being spent and saved could be incorporated into the Number and Operations strand (see 2.4C).

Explaining savings and spending will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 3.9C.

2.11C: distinguish between a deposit and a withdrawal

Students will decipher between deposits (funds placed in to an account) and withdraw (funds moved from an account). Providing real world second grade examples of a deposit and a withdrawal will

Distinguishing between a deposit and a withdrawal will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE, when paired with 2.1A, may introduce students to banking. This SE builds to 6.14A and 6.14C.

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allow students to relate to the state expectation (i.e. Joshua’s dad deposits $20 into Joshua’s school lunch account. Every time that Joshua eats lunch at school, the school withdrawals $2 from the account). Story problems involving real world situations of money being deposited and withdrawn could be incorporated into the Number and Operations strand.

2.11D: identify examples of borrowing and distinguish between responsible and irresponsible borrowing

Providing real world second grade examples of borrowing will allow students to relate to the state expectation (i.e. borrowing a pencil from a friend, borrowing a dollar from your mom, borrowing a video game from a brother, etc.). Classroom discussion should extend to the difference between responsible and irresponsible borrowing (i.e. Responsible borrowing means returning the item in a timely manner and returning the item in good condition. Irresponsible borrowing means not returning the item, not returning the item in a timely manner, returning the item damaged, or losing the item).

Understanding the role of a responsible borrower will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 3.9D.

2.11E: identify examples of lending and use concepts of benefits and costs to evaluate lending decisions

Providing real world second grade examples of lending will allow students to relate to the state expectation (i.e. lending a pencil to a classmate, lending a dollar to your best friend, lending a video game to your brother, etc.). Classroom discussion should extend to the difference between the benefits and costs to lending (i.e. benefits: make a new friend, earn interest on the money lent; get to play the video game with someone instead of alone) and costs (i.e. not having enough money for school supplies or not being able to play a video game).

Identifying the benefits and costs to lending will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

Any calculations should not include interest. This SE builds to 3.9D.

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2.11F: differentiate between producers and consumers and calculate the cost to produce a simple item

This supporting standard serves as an informal study of producers and consumers in terms of economics. Instruction should make connections to those terms in relationship to the real world (i.e. People are consumers as they buy groceries from the producer, our local grocery store. The grocery store becomes the consumer as they rely on the local farmers for their product, etc.). Classroom discussions can then lead to the costs involved for producers to make simple items (i.e. The production of shoes includes the cost of leather, laces, rubber, dye, design, advertisement, shoe salesman, etc.). Perhaps, story problems involving real world situations of the cost to produce simple items could be incorporated into the Number and Operations strand.

Understanding the difference between producers and consumers and calculating the cost to produce a simple item will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

Simple items may include items such as a shirt, a pitcher of lemonade, or a class art project. This SE builds to 3.9A.

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Course: Grade 2 Math Bundle 13: Extended Learning

Dates: May 22nd -June 1st (8 days)

TEKS Continued Problem Solving 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms 2.4D: generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 Continued Number Sense 2.2A: use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones 2.4A: recall basic facts to add and subtract within 20 with automaticity 2.4B: add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations 2.4C: solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms Project Based Learning -Introduce project-based learning activities with strong integration of TEKS that need extended exposure for mastery.

Grade 2 Mathematics Curriculum Document 2016-2017

Documents

Transcript of Grade 2 Mathematics Curriculum Document 2016-2017